Coordinate-space and Observation-space Filtering Methods for Sidereally Repeating Errors in GPS: Performance and Filter Lifetime

Multipath is a major error in GPS observations because it is not removed using differencing techniques. One can benefit from the repetition of satellite-receiver geometry every near sidereal day and apply filtering to minimize this error. For 1 second GPS data, a 10-hour window leads to a consistent and steady value of the geometry-repeat lag, when compared to a window as short as 2 hours giving fluctuating lag values. We conclude that there is little advantage in using a satellite-specific or other timevarying lag in double-difference processing. GPS data is filtered either by stacking and applying number of days of processed coordinate residuals (“coordinate-space filtering”), or double-difference phase residuals (“observation-space filtering”), using the optimum nearsidereal lag (23h 55m 54s). Both methodologies result in a more homogeneous set of coordinates compared with unfiltered processing. Coordinate filtering gives higher precision than observation filtering, but with similar hourto- hour consistency. While stacking three prior days’ data in a high multipath environment, the 24 hour percentage variance reduction reaches 73% for coordinate filtering, where as for observation filtering the corresponding value is 71%. However, the latter technique is advantageous in the less processing time required to achieve filtered coordinates. Thus, the optimal filtering method to use will depend on whether precision or computational time is the over-riding criterion. When using a 3-day stack to form the filter, as the time gap between the days forming the filter and the applied day increases, the final precision worsens gradually. This trend continues until about 23-30 days from the applied day, at which point the precision is the same as the unfiltered case. In competition with this “filter lifetime” effect, stacking more data improves the filter. Stacking 7 days immediately before the applied day results in the best possible precision for both coordinatespace and observation-space filtering. The former methodology reduces the variance of the 24-hour data set by 61%, while the latter has a slightly poorer variance reduction of 52%.